124 A History ofMathematics
should be made:- Islam did certainly differ from Christianity (for example) in the value placed on knowledge, as
the quote above illustrates; and the language of the Qur’an itself is strongly centred on appeals
to reason:
The Koran is a holy book in which rationality plays a big part. In it, Allah is continually arguing and reasoning.
(Rodinson 1974, p. 78 (see also the following pages))
(The reason in question, though, can hardly be equated with mathematical deduction; it is
rather the deduction of our obligations to God from the beneficence of his works, and of ethical
duties from basic principles.) - Høyrup’s point, cited in Section 4: by the ninth century at least, Islam had become codified as a
complete system of practice, organizing every sphere of human action; from which the needs
not simply for knowledge in itself, but for knowledge to inform practice followed.
Rashed’s very recent interview provides some starting points. By claiming that the values of
Islam are specifically favourable to science, he raises the stakes, and makes some statements which
even those who are quite committed to promoting better understanding of Islamic science might
find difficult to accept. The whole interview is worth reading, since as a scholar he cannot only score
good debating points but consider difficult questions such as the ‘decline’ of Islamic mathematics
after the fifteenth century (how can it be understood and accounted for?). And he makes a more
limited but important point, which has indeed been well appreciated, for example, by Kennedy
(1983), that time has a particular value in Islamic observances which calls (one would think) for
the application of science.Science was an important dimension of the Islamic city. One element was the time-keeping (miqat) in the mosques.
Astronomy was necessary to view the lunar crescent for religious purposes. It must not be forgotten that each of the
large mosques had an astronomer associated with it...(Rashed 2003)In fact, few religions have given practical mathematicians so much to think about as Islam, with
its lunar months which start at the moment when the new crescent is visible, its carefully defined
five prayer-times a day, and its fast which ends at dusk. Astronomers worked tirelessly on the
improvement of their tables, developing the Ptolemaic and Hindu astronomy into a much more
efficient instrument; but as early as the time of Th ̄abit ibn Qurra, who wrote on the difficult
question of the first visibility of the moon’s crescent, they came to realize that their under-
standing of atmospheric phenomena always left some doubt about the key questions of what one
could see.
The science of time was of course useful beyond a religious context, and similarly mathematics
was important to the flourishing societies throughout the Islamic world insofar as it helped with
commerce, surveying, architecture, and the various practical arts; and also in geography, the
understanding of the known world. In this religion enters again, and the tenth-century univer-
salist al-B ̄ir ̄un ̄i can stand as a central figure, whoseCoordinates of Citiesmade possible a general
understanding of how the various widely scattered centres were related on the globe, using a
well-developed understanding of geometry on a sphere. Both al-B ̄ir ̄un ̄i and his modern comment-
ators have claimed more; that such knowledge was essential for religious purposes, since to design
the layout of a mosque (say in Seville) correctly it was essential to determine theqibla, the direction